Algorithms for Stochastically Rounded Elementary Arithmetic Operations in IEEE 754 Floating-Point Arithmetic

We present algorithms for performing the five elementary arithmetic operations ( $+$ , notation="LaTeX">$-$ ×, notation="LaTeX">$\div$ and notation="LaTeX">$\sqrt{\phantom{x}}$ ) in floating point with stochastic rounding, demonstrate value of these by discussing various applications where rounding is beneficial. The require that hardware be compliant IEEE 754 floating-point standard a pseudorandom number generator available. goal techniques to emulate when underlying does not support this mode, as case most existing CPUs GPUs. By simulating software, one has possibility explore behavior mode develop new even without having access implementing rounding—once such becomes available, it suffices replace proposed calls corresponding routines. When stochastically double precision operations, we propose are between 7.3 19 times faster than implementations use GNU MPFR library simulate extended precision. test our on tasks, including summation solvers ordinary differential equations, expected bring advantages.